Systems of Equations — Core Skills

The core idea, one worked example, and short practice.

Written and reviewed by the Study Mondo Education TeamLast updated August 21, 2026

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Systems of Equations: The Basics

A system is two equations that are true at the same time. They share the same $x$ and the same $y$ . The solution is the one pair of numbers that makes both equations true, and it is written as a point, $(x, y)$ .

There are two methods you need. The first is substitution. Use it when one equation already tells you what a variable equals, like $y = 4$ or $y = 3x$ . Put that value into the other equation in place of the variable, then solve for the letter that is left.

The second method is adding the equations. Use it when one equation has a plus $y$ and the other has a minus $y$ . Stack them and add straight down. The $y$ terms cancel, leaving one easy equation.

Once you know one variable, put it back into either equation to find the other.

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The core idea, one worked example, and short practice.

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Systems of Equations — Core Skills is part of the SAT Prep course on Study Mondo, specifically in the SAT Core Skills Track section. You can explore the full course for more related topics and practice resources.